ABSTRACT
The process of interest - the system process X - is unobservable. We can
observe the (observation) process Y - a (known) function h of X - which in addition is corrupted by noise N. We want to filter out the noise N from
the observations Y and get an estimate of the process X. This is filtering theory. The filtering model can be written as
The best estimate of X is the conditional distribution of Xt given the
observations upto time t - {Ys;0 s t}. This is called the optimal filter and is denoted by t.
